Reactants ordering

The functional dependence of the half-life on reactant concentration varies with the reactant order. From the integrated rate equations we obtain these results ... 

NO concentrations are doubled, the rate increases by a factor of 8. What are (a) the reactant orders, (b) the overall order of the reaction, and (c) the units of k if the rate is expressed in moles per liter per second ... 

Self-Test 13.3B When the concentration of 2-bromo-2-methylpropane, C4HgBr, is doubled, the rate of the reaction C4H9Br(aq) + OH (aq) - C4HgOH(aq) + P>r (aq) increases by a factor of 2. When both the C4HgBr and the OH- concentrations are doubled, the rate increase is the same, a factor of 2. What are (a) the reactant orders, (b) the overall order of the reaction, and (c) the units of k if the rate is expressed in moles per liter per second ... 

Use of experimental data and graphical analysis to determine reactant order, rate constants, and reaction rate laws... 

Combining these reactant orders in a rate equation gives... 

The resulting equation is consistent with all observed reactant orders suggesting that a formate-based mechanism applies. 

Combining these reactant orders in a rate equation gives rate = [X] [Y]" = X] ... 

In the study of this reaction it is important again to take into account the adsorption of reactant ketone molecules and the intermediate in interpretations (cf. Ref 147) of the reactant order and thence the assignment of reaction... 

Order with respect to the reactant. Order with respect to H. ... 

When BPA is reacted with ECH, several polymeric and non-polymeric products may be formed depending on reaction conditions ratio of reactants, order of addition, temperature, and residence time at the temperature. That is, all of the information contained in a typical process description may be needed to determine the chemical identity of the reaction product(s). 

Nonetheless, rate expressions more complex than a simple power law are sometimes useful. For example, a power law expression does not provide any insight into the reasons for changing reactant order (i.e., a changing value of a ) with temperature or organic reactant concentration. However, such effects are frequently observed in oxidation reactions and are often consistent with more fundamentally based rate expressions. Consider, for example, what one would suppose to be the simple oxidation of methane. Golodets (p. 445) states that methane oxidation over metal oxide catalysts may be interpreted by the following mechanism ... 

Conventional kinetic analysis of the reactions of NM, nitroethane (NE), and 2-nitropropane (2-NP) with hydroxide ion in water revealed that the reactions are complex and involve kinetically significant intermediates. The deviations from first-order kinetics were observed to increase with increasing extent of reaction and in the reactant order NM < NE < 2-NP. The apparent deuterium kinetic isotope effects for proton/deuteron transfer approach unity near zero time and increase with time towards plateau values as the reaction kinetics reach steady state. 

The powers to which the concentrations are raised, x and y, are usually small integers or zero but are occasionally fractional or even negative. A power of one means that the rate is directly proportional to the concentration of that reactant. A power of two means that the rate is direcdy proportional to the square of that concentration. A power of zero means that the rate does not depend on the concentration of that reactant, so long as some of the reactant is present. The value of x is said to be the order of the reaction with respect to A, and 3/ is the order of the reaction with respect to B. The overall order of the reaction is the sum of the reactant orders, x + y. Examples of observed rate laws for some reactions follow. 

Although we will usually work with simple integer values for reactant orders, fractional values can occur. For fractional orders the value cannot be determined quite so simply. In the previous example, if doubling the concentration of [A] changed the rate by a factor of 2.83 we would have ... 

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